## Presentation on theme: "Radicals Review."— Presentation transcript:

Pronounced: 2 times the square root of 7 OR 2 radical 7

Simplest Radical Form When you cannot factor any more perfect squares from the radicand The radical cannot be simplified further We always want our answers to be in simplest radical form

Steps 1. Look for the largest perfect square that’s a factor of the radicand.

Steps 2. Factor using the perfect square as one of the factors.

Steps 3. Take the square root of the factor that’s a perfect square. 4

Steps 4. Write the square root as the factor in front of the radical and leave the other factor under the radical.

Steps 5. If there’s a number in front of the radical, multiply the square root by it. 3

Always check if the radicand is perfect square! Check if factorable by common perfect squares – 4, 9, 16, or 25 If the radicand is prime (or if its only factors are prime), then it’s in simplest radical form Be persistent! You don’t have to find the largest perfect square the first time you factor the radicand

Examples

Examples

Examples

Or… 3 25 𝑥 6

Or Even… 5𝑥 32 𝑥 11

Your Turn: 3 48 𝑚 7 𝑥 3 𝑦 5

Examples

Examples

Examples

Seek and Solve!!!

What is rationalizing? The process of algebraically removing a radical sign from one part of a fraction We generally rationalize the denominator (But we can rationalize the numerator.)

Why rationalize? The result is easier to estimate and understand
Also shows up in solving limits (in calculus)

An expression with exactly one term
Monomial An expression with exactly one term Examples: 3x –7x3 Non-Examples: 7x – 4 4y2 – 16y + 60

Rationalizing the Numerator
Exact same process as rationalizing the denominator, except that we focus on the numerator instead of the denominator. Reappears in calculus